Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager’s results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems—deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems—provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here.

We study electron transport through a single-molecule magnet (SMM) and the interplay of its anisotropic spin with quantized vibrational distortions of the molecule. Based on numerical renormalization group calculations we show that, despite the longitudinal anisotropy barrier and small transverse anisotropy, vibrational fluctuations can induce quantum spin-tunneling (QST) and a QST-Kondo effect. The interplay of spin scattering, QST and molecular vibrations can strongly enhance the Kondo effect and induce an anomalous magnetic field dependence of vibrational Kondo side-bands.

In this article we review aspects of charge and heat transport in interacting quantum dots and molecular junctions under stationary and time-dependent non-equilibrium conditions due to finite electrical and thermal bias. In particular, we discuss how a discrete level spectrum can be beneficial for thermoelectric applications, and investigate the detrimental effects of molecular vibrations on the efficiency of a molecular quantum dot as an energy converter. In addition, we consider the effects of a slow time-dependent modulation of applied voltages on the transport properties of a quantum dot and show how this can be used as a spectroscopic tool complementary to standard dc-measurements. Finally, we combine time-dependent driving with thermoelectrics in a double-quantum dot system - a nanoscale analogue of a cyclic heat engine - and discuss its operation and the main limitations to its performance.